NAG Library Chapter Contents

S ()
Approximations of Special Functions


S (specfun) Chapter Introduction – a description of the Chapter and an overview of the algorithms available

Routine
Name
Mark of
Introduction

Purpose
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Example Text
Example Data
14 nagf_specfun_log_shifted
ln1+x
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Example Data
14 nagf_specfun_exp_complex
Complex exponential, ez
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1 nagf_specfun_tan
tanx
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1 nagf_specfun_arcsin
arcsinx
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3 nagf_specfun_arccos
arccosx
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3 nagf_specfun_tanh
tanhx
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4 nagf_specfun_sinh
sinhx
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4 nagf_specfun_cosh
coshx
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4 nagf_specfun_arctanh
arctanhx
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4 nagf_specfun_arcsinh
arcsinhx
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4 nagf_specfun_arccosh
arccoshx
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Example Plot
1 nagf_specfun_integral_exp
Exponential integral E1x
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Example Plot
2 nagf_specfun_integral_cos
Cosine integral Cix
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5 nagf_specfun_integral_sin
Sine integral Six
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1 nagf_specfun_gamma
Gamma function
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Example Plot
8 nagf_specfun_gamma_log_real
Log gamma function, real argument
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14 nagf_specfun_polygamma
ψx-lnx
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14 nagf_specfun_polygamma_deriv
Scaled derivatives of ψx
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20 nagf_specfun_psi_deriv_real
Polygamma function ψnx for real x
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20 nagf_specfun_psi_deriv_complex
Polygamma function ψnz for complex z
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21 nagf_specfun_gamma_log_complex
Logarithm of the gamma function lnΓz, complex argument
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23 nagf_specfun_gamma_log_scaled_real
Scaled log gamma function
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14 nagf_specfun_gamma_incomplete
Incomplete gamma functions Pa,x and Qa,x
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24 nagf_specfun_beta_log_real
Logarithm of the beta function lnBa,b
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24 nagf_specfun_beta_incomplete
Incomplete beta function Ixa,b and its complement 1-Ix
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3 nagf_specfun_cdf_normal
Cumulative Normal distribution function Px
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4 nagf_specfun_compcdf_normal
Complement of cumulative Normal distribution function Qx
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4 nagf_specfun_erfc_real
Complement of error function erfcx
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4 nagf_specfun_erf_real
Error function erfx
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7 nagf_specfun_dawson
Dawson's integral
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22 nagf_specfun_erfcx_real
Scaled complement of error function, erfcxx
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14 nagf_specfun_erfc_complex
Scaled complex complement of error function, exp-z2erfc-iz
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Example Plot
1 nagf_specfun_bessel_y0_real
Bessel function Y0x
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1 nagf_specfun_bessel_y1_real
Bessel function Y1x
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5 nagf_specfun_bessel_j0_real
Bessel function J0x
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5 nagf_specfun_bessel_j1_real
Bessel function J1x
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Example Plot
8 nagf_specfun_airy_ai_real
Airy function Aix
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Example Plot
8 nagf_specfun_airy_bi_real
Airy function Bix
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Example Plot
8 nagf_specfun_airy_ai_deriv
Airy function Aix
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Example Plot
8 nagf_specfun_airy_bi_deriv
Airy function Bix
s17alf
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20 nagf_specfun_bessel_zeros
Zeros of Bessel functions Jαx, Jαx, Yαx or Yαx
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24 nagf_specfun_bessel_y0_real_vector
Bessel function vectorized Y0x
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24 nagf_specfun_bessel_y1_real_vector
Bessel function vectorized Y1x
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24 nagf_specfun_bessel_j0_real_vector
Bessel function vectorized J0x
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24 nagf_specfun_bessel_j1_real_vector
Bessel function vectorized J1x
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24 nagf_specfun_airy_ai_real_vector
Airy function vectorized Aix
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24 nagf_specfun_airy_bi_real_vector
Airy function vectorized Bix
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24 nagf_specfun_airy_ai_deriv_vector
Derivatives of the Airy function, vectorized Aix
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24 nagf_specfun_airy_bi_deriv_vector
Derivatives of the Airy function, vectorized Bix
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13 nagf_specfun_bessel_y_complex
Bessel functions Yν+az, real a0, complex z, ν=0,1,2,
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13 nagf_specfun_bessel_j_complex
Bessel functions Jν+az, real a0, complex z, ν=0,1,2,
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13 nagf_specfun_airy_ai_complex
Airy functions Aiz and Aiz, complex z
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13 nagf_specfun_airy_bi_complex
Airy functions Biz and Biz, complex z
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13 nagf_specfun_hankel_complex
Hankel functions Hν+ajz, j=1,2, real a0, complex z, ν=0,1,2,
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Example Plot
26.1 nagf_specfun_struve_h0
Struve function of order 0, H0x
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Example Plot
26.1 nagf_specfun_struve_h1
Struve function of order 1, H1x
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Example Plot
1 nagf_specfun_bessel_k0_real
Modified Bessel function K0x
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1 nagf_specfun_bessel_k1_real
Modified Bessel function K1x
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5 nagf_specfun_bessel_i0_real
Modified Bessel function I0x
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5 nagf_specfun_bessel_i1_real
Modified Bessel function I1x
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24 nagf_specfun_bessel_k0_real_vector
Modified Bessel function vectorized K0x
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24 nagf_specfun_bessel_k1_real_vector
Modified Bessel function vectorized K1x
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24 nagf_specfun_bessel_i0_real_vector
Modified Bessel function vectorized I0x
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24 nagf_specfun_bessel_i1_real_vector
Modified Bessel function vectorized I1x
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10 nagf_specfun_bessel_k0_scaled
Scaled modified Bessel function exK0x
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10 nagf_specfun_bessel_k1_scaled
Scaled modified Bessel function exK1x
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10 nagf_specfun_bessel_i0_scaled
Scaled modified Bessel function e-xI0x
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10 nagf_specfun_bessel_i1_scaled
Scaled modified Bessel function e-xI1x
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24 nagf_specfun_bessel_k0_scaled_vector
Scaled modified Bessel function vectorized exK0x
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24 nagf_specfun_bessel_k1_scaled_vector
Scaled modified Bessel function vectorized exK1x
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24 nagf_specfun_bessel_i0_scaled_vector
Scaled modified Bessel function vectorized e-xI0x
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24 nagf_specfun_bessel_i1_scaled_vector
Scaled modified Bessel function vectorized e-xI1x
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13 nagf_specfun_bessel_k_complex
Modified Bessel functions Kν+az, real a0, complex z, ν=0,1,2,
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13 nagf_specfun_bessel_i_complex
Modified Bessel functions Iν+az, real a0, complex z, ν=0,1,2,
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Example Plot
26.1 nagf_specfun_struve_l0
Modified Struve function of order 0, L0x
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Example Plot
26.1 nagf_specfun_struve_l1
Modified Struve function of order 1, L1x
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Example Plot
26.1 nagf_specfun_struve_i0ml0
The function I0x-L0x, where I0x is a modified Bessel function and L0x is a Struve function
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Example Plot
26.1 nagf_specfun_struve_i1ml1
The function I1x-L1x, where I1x is a modified Bessel function and L1x is a Struve function
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21 nagf_specfun_bessel_j_seq_complex
Bessel function of the 1st kind Jα±nz
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11 nagf_specfun_kelvin_ber
Kelvin function berx
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11 nagf_specfun_kelvin_bei
Kelvin function beix
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11 nagf_specfun_kelvin_ker
Kelvin function kerx
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11 nagf_specfun_kelvin_kei
Kelvin function keix
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24 nagf_specfun_kelvin_ber_vector
Kelvin function vectorized berx
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Example Data
24 nagf_specfun_kelvin_bei_vector
Kelvin function vectorized beix
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24 nagf_specfun_kelvin_ker_vector
Kelvin function vectorized kerx
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24 nagf_specfun_kelvin_kei_vector
Kelvin function vectorized keix
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Example Plot
5 nagf_specfun_fresnel_s
Fresnel integral Sx
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Example Plot
5 nagf_specfun_fresnel_c
Fresnel integral Cx
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24 nagf_specfun_fresnel_s_vector
Fresnel integral vectorized Sx
s20arf
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Example Data
24 nagf_specfun_fresnel_c_vector
Fresnel integral vectorized Cx
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8 nagf_specfun_ellipint_symm_1_degen
Degenerate symmetrised elliptic integral of 1st kind RCx,y
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8 nagf_specfun_ellipint_symm_1
Symmetrised elliptic integral of 1st kind RFx,y,z
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8 nagf_specfun_ellipint_symm_2
Symmetrised elliptic integral of 2nd kind RDx,y,z
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8 nagf_specfun_ellipint_symm_3
Symmetrised elliptic integral of 3rd kind RJx,y,z,r
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Example Plot
22 nagf_specfun_ellipint_legendre_1
Elliptic integral of 1st kind, Legendre form, Fϕm
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Example Plot
22 nagf_specfun_ellipint_legendre_2
Elliptic integral of 2nd kind, Legendre form, E ϕm
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22 nagf_specfun_ellipint_legendre_3
Elliptic integral of 3rd kind, Legendre form, Π n;ϕm
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22 nagf_specfun_ellipint_complete_1
Complete elliptic integral of 1st kind, Legendre form, K m
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22 nagf_specfun_ellipint_complete_2
Complete elliptic integral of 2nd kind, Legendre form, E m
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15 nagf_specfun_jacellip_real
Jacobian elliptic functions sn, cn and dn of real argument
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20 nagf_specfun_jacellip_complex
Jacobian elliptic functions sn, cn and dn of complex argument
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20 nagf_specfun_jactheta_real
Jacobian theta functions θkx,q of real argument
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20 nagf_specfun_ellipint_general_2
General elliptic integral of 2nd kind Fz,k,a,b of complex argument
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20 nagf_specfun_legendre_p
Legendre functions of 1st kind Pnmx or Pnm¯x
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24 nagf_specfun_1f1_real
Real confluent hypergeometric function F 1 1 a;b;x
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24 nagf_specfun_1f1_real_scaled
Real confluent hypergeometric function F 1 1 a;b;x  in scaled form
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25 nagf_specfun_2f1_real
Real Gauss hypergeometric function F1 2 a,b;c;x
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25 nagf_specfun_2f1_real_scaled
Real Gauss hypergeometric function F 1 2 a,b; c;x  in scaled form
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Example Data
22 nagf_specfun_opt_bsm_price
Black–Scholes–Merton option pricing formula
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Example Data
22 nagf_specfun_opt_bsm_greeks
Black–Scholes–Merton option pricing formula with Greeks
s30baf
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Example Data
22 nagf_specfun_opt_lookback_fls_price
Floating-strike lookback option pricing formula in the Black-Scholes-Merton model
s30bbf
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Example Data
22 nagf_specfun_opt_lookback_fls_greeks
Floating-strike lookback option pricing formula with Greeks in the Black-Scholes-Merton model
s30caf
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Example Data
22 nagf_specfun_opt_binary_con_price
Binary option, cash-or-nothing pricing formula
s30cbf
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22 nagf_specfun_opt_binary_con_greeks
Binary option, cash-or-nothing pricing formula with Greeks
s30ccf
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22 nagf_specfun_opt_binary_aon_price
Binary option, asset-or-nothing pricing formula
s30cdf
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22 nagf_specfun_opt_binary_aon_greeks
Binary option, asset-or-nothing pricing formula with Greeks
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22 nagf_specfun_opt_barrier_std_price
Standard barrier option pricing formula
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22 nagf_specfun_opt_jumpdiff_merton_price
Jump-diffusion, Merton's model, option pricing formula
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22 nagf_specfun_opt_jumpdiff_merton_greeks
Jump-diffusion, Merton's model, option pricing formula with Greeks
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22 nagf_specfun_opt_heston_price
Heston's model option pricing formula
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23 nagf_specfun_opt_heston_greeks
Heston's model option pricing formula with Greeks
s30ncf
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25 nagf_specfun_opt_heston_term
Heston's model option pricing with term structure
s30qcf
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Example Data
22 nagf_specfun_opt_amer_bs_price
American option, Bjerksund and Stensland pricing formula
s30saf
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Example Data
22 nagf_specfun_opt_asian_geom_price
Asian option, geometric continuous average rate pricing formula
s30sbf
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Example Data
22 nagf_specfun_opt_asian_geom_greeks
Asian option, geometric continuous average rate pricing formula with Greeks
© The Numerical Algorithms Group Ltd, Oxford, UK. 2017